Heat the olive oil in a Dutch oven or braising pot over medium heat. Once hot, add mushrooms and cook until glossy, about 3-4 minutes. Add the garlic and cook until fragrant, about 1-2 minutes longer.
Add the gochujang and stir well to combine. Once combined and beginning to stick to the bottom of the pot, add the lemon juice, vegetable broth, soy sauce, miso, and cumin. Whisk to combine the miso into the broth, then bring to a simmer.
Add the parsnips, submerging as much as possible. Carefully stir the parsnips to coat each one in broth, then cover the pot and turn the heat to medium-low. Cook for 1 hour, or until the parsnips on top are very soft.
Once the parsnips are fork tender, remove the lid and cook for another 30-40 minutes, until the broth is reduced to a thick sauce. To serve, ladle parsnips and mushrooms over rice, if desired, then ladle the sauce over the parsnips.